相关论文: Framed Hitchin Pairs

A flat complex vector bundle (E,D) on a compact Riemannian manifold (X,g) is stable (resp. polystable) in the sense of Corlette [C] if it has no D-invariant subbundle (resp. if it is the D-invariant direct sum of stable subbundles). It has…

Let $C$ be a smooth projective curve of genus $g\geq 2$ over $\mathbb C$. Fix $n\geq 1$, $d\in {\mathbb Z}$. A pair $(E,\phi)$ over $C$ consists of an algebraic vector bundle $E$ of rank $n$ and degree $d$ over $C$ and a section $\phi \in…

In the study of automorphic representations over a function field, Hitchin moduli stack and its variants naturally appear and their geometry helps the comparison of trace formulae. We give a survey on applications of this observation to a…

We prove the Topological Mirror Symmetry Conjecture by Hausel-Thaddeus for smooth moduli spaces of Higgs bundles of type $\operatorname{SL}_n$ and $\operatorname{PGL}_n$. More precisely, we establish an equality of stringy Hodge numbers for…

We prove homological stability for both general linear groups of modules over a ring with finite stable rank and unitary groups of quadratic modules over a ring with finite unitary stable rank. In particular, we do not assume the modules…

The Minimal Model Program offers natural higher-dimensional analogues of stable $n$-pointed curves and maps: stable pairs consisting of a projective variety $X$ of dimension $\ge2$ and a divisor $B$, that should satisfy a few simple…

We prove the existence of a Hermitian-Einstein metric on holomorphic vector bundles with a Hermitian metric satisfying the analytic stability condition, under some assumption for the underlying K\"ahler manifolds. We also study the…

We prove a rigidity result for automorphisms of points of certain stacks admitting adequate moduli spaces. It encompasses as special cases variations of the moduli of $G$-bundles on a smooth projective curve for a reductive algebraic group…

For $L \hookrightarrow X$ a Lagrangian embedding associated with a real homogeneous space, we construct the moduli space of stable holomorphic discs mapping to $(X,L)$ as an orbifold with corners equipped with a group action. Some essential…

Moduli spaces - finite-dimensional, collective coordinate manifolds - for kinks and antikinks in $\phi^4$ theory and sine-Gordon theory are reconsidered. The field theory Lagrangian restricted to moduli space defines a reduced Lagrangian,…

We introduce moduli spaces of quasi-admissible hyperelliptic covers with at worst A and D singularities. The stability conditions for these moduli spaces depend on two parameters describing allowable singularities. By varying these…

The Tamari lattice and the associahedron provide methods of measuring associativity on a line. The real moduli space of marked curves captures the space of such associativity. We consider a natural generalization by considering the moduli…

A twisted quiver bundle is a set of holomorphic vector bundles over a complex manifold, labelled by the vertices of a quiver, linked by a set of morphisms twisted by a fixed collection of holomorphic vector bundles, labelled by the arrows.…

For any rigid space over a perfectoid extension of $\mathbb Q_p$ that admits a liftable smooth formal model, we construct an isomorphism between the moduli stacks of Hitchin-small Higgs bundles and Hitchin-small v-vector bundles. This…

The homology of configuration spaces of point-particles in manifolds has been studied intensively since the 1970s; in particular it is known to be stable if the underlying manifold is connected and open. Closely related to configuration…

We construct new moduli spaces of quiver representations with multiplicities, i.e. over rings of truncated power series. This includes moduli of framed representations and analogues of Nakajima quiver varieties. Our construction relies on…

We compute the anomalies of the topological A and B models with target space geometry of Hitchin's generalized type. The dimension of the moduli space of generalized holomorphic maps is also computed, which turns out to be equal to the…

The geometry of the moduli space of stable spin curves is studied, with emphasis on its combinatorial properties. In this context, the standard graph theoretic framework is not just a book-keeping device: some purely combinatorial results…

Hamiltonian structures for spatially compact locally homogeneous vacuum universes are investigated, provided that the set of dynamical variables contains the \Teich parameters, parameterizing the purely global geometry. One of the key…

We construct a moduli space that parametrises stable proper holomorphic submersions over a fixed compact Kaehler base. Stability is described in terms of the existence of a canonical relatively Kaehler metric on the submersion, called an…